A note on the weak Lefschetz property of monomial complete intersections in positive characteristic

DOI10.1007/s13348-010-0006-8zbMath1221.13019arXiv1003.0824OpenAlexW2016624545MaRDI QIDQ2430587

Holger Brenner, Almar Kaid

Publication date: 8 April 2011

Published in: Collectanea Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.0824

zbMATH Keywords

syzygyweak Lefschetz propertystable bundlemonomial complete intersectionartinian algebraGrauert-Mülich theorem

Mathematics Subject Classification ID

Vector bundles on surfaces and higher-dimensional varieties, and their moduli (14J60) Linkage, complete intersections and determinantal ideals (13C40) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Syzygies, resolutions, complexes and commutative rings (13D02) Commutative Artinian rings and modules, finite-dimensional algebras (13E10) Other special types of modules and ideals in commutative rings (13C13)

Related Items (24)

The weak Lefschetz property for monomial ideals of small type ⋮ The Weak Lefschetz Property for monomial complete intersection in positive characteristic ⋮ Monomial ideals and the failure of the strong Lefschetz property ⋮ Monomial complete intersections, the weak Lefschetz property and plane partitions ⋮ Asymptotic behavior of the socle of Frobenius powers ⋮ Trivariate monomial complete intersections and plane partitions ⋮ The weak Lefschetz property of Gorenstein algebras of codimension three associated to the Apéry sets ⋮ Syzygy gap fractals. I: Some structural results and an upper bound ⋮ Forcing the weak Lefschetz property for equigenerated monomial ideals ⋮ The Lefschetz properties of monomial complete intersections in positive characteristic ⋮ The resolution of the bracket powers of the maximal ideal in a diagonal hypersurface ring ⋮ Hyperplane sections and the subtlety of the Lefschetz properties ⋮ On the degrees of relations on \(x_1^{d_1}, \dots, x_n^{d_n},(x_1 + \dots + x_n)^{d_{n + 1}}\) in positive characteristic ⋮ Syzygy bundles and the weak Lefschetz property of monomial almost complete intersections ⋮ On the structure of monomial complete intersections in positive characteristic ⋮ On the weak Lefschetz property for artinian Gorenstein algebras of codimension three ⋮ Artinian Gorenstein algebras with linear resolutions ⋮ The weak Lefschetz property for Artinian Gorenstein algebras of codimension three ⋮ Algebraic stories from one and from the other pockets ⋮ The Lefschetz question for ideals generated by powers of linear forms in few variables ⋮ A note on a conjecture regarding the weak Lefschetz property of a special class of Artinian algebras ⋮ Hilbert functions of Artinian Gorenstein algebras with the strong Lefschetz property ⋮ Artinian algebras and Jordan type ⋮ An Artinian Quotient of the Coordinate Ring of a Complete Intersection in ℙⁿHaving the Weak Lefschetz Property

Cites Work

• Unnamed Item
• Monomial complete intersections, the weak Lefschetz property and plane partitions
• Syzygy bundles on \(\mathbb P^2\) and the weak Lefschetz property
• Looking out for stable syzygy bundles
• The weak and strong Lefschetz properties for Artinian \(K\)-algebras
• Mason's theorem and syzygy gaps
• Monomial ideals, almost complete intersections and the Weak Lefschetz property

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